Results 41 to 50 of about 4,343 (225)
Abstract 3-Rigidity and Bivariate $C_2^1$-Splines I: Whiteley's Maximality Conjecture
Discrete Analysis, 2022 3-Rigidity and Bivariate $C_2^1$-Splines I: Whiteley's Maximality Conjecture, Discrete Analysis 2022:2, 50 pp. Suppose one realizes a graph $G$ by taking its vertex set to be a set of points $x_1,\dots,x_n$ in $\mathbb R^d$ and the edge joining $x_i$ to
Katie Clinch +2 more
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The structure of equivalent 3-separations in a 3-connected matroid [PDF]
, 2004 For the abstract of this paper, please see the PDF ...
Oxley, James +11 more
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$Star^1$-convex functions on tropical linear spaces of complete graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Given a fan $\Delta$ and a cone $\sigma \in \Delta$ let $star^1(\sigma )$ be the set of cones that contain $\sigma$ and are one dimension bigger than $\sigma$ . In this paper we study two cones of piecewise linear functions defined on $\delta$ : the cone
Laura Escobar
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Representing Matroids over the Reals is $\exists \mathbb R$-complete [PDF]
Discrete Mathematics & Theoretical Computer ScienceA matroid $M$ is an ordered pair $(E,I)$, where $E$ is a finite set called the ground set and a collection $I\subset 2^{E}$ called the independent sets which satisfy the conditions: (i) $\emptyset \in I$, (ii) $I'\subset I \in I$ implies $I'\in I$, and ...
Eun Jung Kim +2 more
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Reducing the rank of a matroid [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We consider the rank reduction problem for matroids: Given a matroid $M$ and an integer $k$, find a minimum size subset of elements of $M$ whose removal reduces the rank of $M$ by at least $k$. When $M$ is a graphical matroid this problem is the minimum $
Gwenaël Joret, Adrian Vetta
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Real phase structures on matroid fans and matroid orientations
, 2023 We introduce the notion of real phase structure on rational polyhedral fans in Euclidean space. Such a structure consists of an assignment of affine spaces over $\mathbb{Z}/2\mathbb{Z}$ to each top dimensional face of the fan subject to two conditions ...
Shaw, Kris +2 more
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Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations
The Scientific World Journal, 2014 Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as ...
Hui Li, Yanfang Liu, William Zhu
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Graphic Splitting of Cographic Matroids
Discussiones Mathematicae Graph Theory, 2015 In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid Mx,y is graphic for every pair x, y of elements of M.
Pirouz Naiyer
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Matroids on the Bases of Simple Matroids
European Journal of Combinatorics, 1981 Let M be a simple matroid (= combinatorial geometry). On the bases of M we consider two matroids S(M, F) and H(M, F), which depend on a field F. S(M, F) is the simplicial matroid with coefficients in F on the bases of M considered as simplices. H(M, F) has been studied by Björner in [1].
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Towards a splitter theorem for internally 4-connected binary matroids
, 2011 This is the post-print version of the Article - Copyright @ 2012 ElsevierWe prove that if M is a 4-connected binary matroid and N is an internally 4-connected proper minor of M with at least 7 elements, then, unless M is a certain 16-element matroid ...
Chun, Carolyn +8 more
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